This invention relates generally to signal processing and, more particularly, to the area of multichannel least squares adaptive filtering.
In many multisensor signal processing applications, e.g., radar/sonar beamforming, magnetoencephalography, seismology data, and the like complete a priori knowledge of the signal environment is lacking and/or the environment is changing. To determine the signal content from the sensor data, least squares-based adapted filters generally provide the best tradeoff between convergence or tracking rate and overall estimation error.
However, like most adaptive filters, conventional least squares adaptive filters require an explicit a priori desired signal for operation. In many applications no desired signal is available. Rather, the a priori knowledge exists in the form of the signal-to-data cross correlation. An example of this is adaptive radar/sonar beam forming in which the cross-correlating corresponds to the known steering vector.
For this class of application, a multiple-input, multiple-output mixed adaptive filter is needed which optimally combines the a priori cross-correlation knowledge with ongoing data measurements. Conventional filters of this class are computationally intensive and their performance is critically dependent on the underlying algorithm. There is no mixed adaptive filter that is based on an algorithm that is (1) efficient and numerically stable and (2) is regularly structured so that the filter can be readily implemented in hardware.
Array hardware architectures are generally designed to reflect the structure of the algorithms to be implemented, where the algorithms are mapped onto the elements of the array and scheduled in the proper order. Adaptive least squares-like algorithms are well-suited to implementation by array hardware architectures because they are characterized by regularity and data independence i.e., the required computations are independent of the actual data to be operated on.
Architectures for handling recursive least squares problems with an explicit desired signal have been proposed and, more particularly. Array architectures based on a QR decomposition followed by a back substitution. W. M. Gentleman et al., "Matrix Triangularization by Systolic Array". SPIE Proc. Real Time Signal Processing IV, p 298 (1981) incorporated herein by reference, proposes an architecture for the non-recursive Givens rotation problem. S. Haykin, Adaptive Filter Theory, Prentice-Hall, Englewood Cliffs, N. J. (1986), describes a recursive RLS-QR architecture that uses back substitution. However, an imbalance arises between the QR update and the back substitution at each step. Global communications are also required between the QR array and the back substitution array. A single channel architecture to calculate an estimation error is described in J. G. McWhirter, "Recursive Least-Squares Minimization Using a Systolic Array", SPIE Proc. Real Time Signal Processing VI p 105 (1983). However, there is no known balanced array architecture which can implement the multichannel mixed adaptive filter for applications in which no explicit desired signal is available.
Magnetoencephalography (MEG), the study of naturally occurring magnetic fields for the brain, provides a particularly difficult signal processing environment. Neuromagnetic fields are quite weak, ranging from 10.sup.-12 to 10.sup.-14 tesla (T). compared with urban background noise, 10.sup.-6 to 10.sup.-7 T. The effect of external magnetic fields on the signal-to-noise ratio is reduced by using magnetically shielded rooms and using sensors wired as first and second order gradiometers, but external and neural noise cannot be eliminated.
To obtain signal information, i.e., evoked response data, signal ensemble averaging is generally used. Measurements from multiple trials using the same stimulus are combined by simply averaging together the measurements from each trial at identical latencies (time delays) from the stimulus. Signal averaging produces optimal results when each evoked response is identical and the noise is additive and uncorrelated from trial to trial. However, evoked responses vary, both in latency and in waveform, so that signal averaging produces a distorted "average" response. Further signal averaging does not permit examination of individual trials and their variation.
These and other signal processing problems of the prior art are addressed by the present invention and improved processing algorithms and array architectures for the mixed adaptive filter are provided with particular application to MEG signal processing.
It is an object of the present invention to provide a signal processing algorithm for the multichannel mixed adaptive filter which is efficient and numerically stable.
It is another object to provide balanced array architectures onto which the signal processing algorithm can be mapped in both multiple and single output cases.
It is one other object of the present invention to provide array architectures with multiple input channel processing capability for estimating both multiple and single channel signal data from sensor output data.
Yet another object of the present invention is to provide for MEG single-trial enhancement utilizing prestimulus data, ensemble average data, or signal autocorrelation data as a priori information.
Additional objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.